US8831885B2 - Integrated radioactive source-free method and apparatus for porosity determination: NMR calibrated acoustic porosity - Google Patents
Integrated radioactive source-free method and apparatus for porosity determination: NMR calibrated acoustic porosity Download PDFInfo
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- This disclosure relates to apparatus and techniques for making porosity measurements of an earth formation without using radioactive sources. Specifically, the disclosure relates to the design of an accurate acoustic measurement technique which, when calibrated with NMR measurements, gives the porosity of an earth formation over a wide range of lithologies and in the presence of gas in the formation.
- Oil well logging has been known for many years and provides an oil and gas well driller with information about the particular earth formation being drilled.
- a probe known as a sonde is lowered into the borehole and used to determine some characteristic of the formations which the well has traversed.
- the probe is typically a hermetically sealed steel cylinder which hangs at the end of a long cable which gives mechanical support to the sonde and provides power to the instrumentation inside the sonde.
- the cable also provides communication channels for sending information up to the surface. It thus becomes possible to measure some parameter of the earth's formations as a function of depth, that is, while the sonde is being pulled uphole.
- Such “wireline” measurements are normally done in real time (however, these measurements are taken long after the actual drilling has taken place).
- Porosity measurements are commonly done by using a dual detector neutron logging tool using a source of neutrons irradiating the formation being studied.
- Density measurements are commonly done by using a dual detector gamma ray logging tool using a source of gamma rays irradiating the formation being studied.
- the density measurements, and some of the porosity measurements may require the use of a radioactive source of neutrons and/or gamma rays. From a safety standpoint, the use of radioactive sources is problematic, particularly for measurement while drilling (MWD) applications.
- MWD measurement while drilling
- Radioactive-source-free tools such as Nuclear Magnetic Resonance (NMR) and acoustic logging have been used in the past for porosity determination.
- NMR logging has the advantage of directly measuring fluids in pore space and, thus, does not suffer from the lithology effect on porosity determination.
- the accuracy of NMR total porosity in gas-bearing formations is affected by low hydrogen index (HI) and the ability to separate gas and liquid NMR responses.
- HI hydrogen index
- the hydrocarbon signals may relax too fast to be observed by the state of art NMR well logging instruments, thereby causing under-estimation of porosity.
- acoustic measurements respond to lithology and texture in addition to porosity. Consequently acoustic porosity is an indirect measurement based on empirical or semi-empirical models, which often requires calibration of model parameters.
- Integrating acoustic and NMR measurements for gas-zone porosity estimation has been reported in relatively clean sandstones.
- the existing methods in literature have not been extended to shaly sandstones.
- the present disclosure describes a radioactive source-free porosity estimation method using NMR logs to calibrate acoustic porosity models. This approach is applicable to clean and shaly sandstones using wireline and logging while drilling (LWD) measurements.
- the present disclosure is directed to a method and apparatus for making porosity measurements of an earth formation without using a radioactive source.
- the present disclosure is directed to acoustic measurements calibrated with NMR measurements and used to estimate porosity of an earth formation over a range of lithologies and in the presence of gas in the formation.
- One embodiment of the disclosure includes a method of estimating a value of a porosity of an earth formation comprising a first solid component, a second solid component, and a gas.
- the method includes: using an acoustic tool for making a measurement indicative of a porosity of the earth formation in an interval that includes (i) a gas, (ii) the first solid component, and (iii) the second solid component; and using a processor for: estimating the value of the porosity in the interval using the measurement made by the acoustic tool, a fractional value of the second component, and at least one parameter relating an additional measurement made by the acoustic tool to a measurement by a nuclear magnetic resonance (NMR) tool in another interval that does not include a gas.
- NMR nuclear magnetic resonance
- Another embodiment of the disclosure includes an apparatus configured to estimate a value of a porosity of an earth formation comprising a first solid component, a second solid component and a gas.
- the apparatus includes: an acoustic tool configured to make a measurement indicative of a porosity of the earth formation in an interval that includes: (i) a gas, (ii) the first solid component, and (iii) the second solid component; and a processor configured to: estimate a value of the porosity in the interval using the measurement made by the acoustic tool, a fractional value of the second component and at least one parameter relating an additional measurement made by the acoustic tool to a measurement by a nuclear magnetic resonance (NMR) tool in another interval that does not include a gas.
- NMR nuclear magnetic resonance
- Another embodiment of the disclosure is a tangible computer-readable medium product having stored thereon instructions what when read by a processor cause the processor to execute a method.
- the method includes: estimating a value of a porosity of a formation, using a measurement made by an acoustic tool in a borehole in an interval containing a first solid component, a second solid component, and a gas; a fractional value of the second component; and at least one parameter relating an additional measurement made by the acoustic tool to a measurement by a nuclear magnetic resonance (NMR) tool in another interval that does not include a gas.
- NMR nuclear magnetic resonance
- FIG. 1 depicts diagrammatically an NMR logging tool in a borehole according to one embodiment of the present disclosure
- FIG. 2 shows plot of ⁇ t ma vs. GR in the water bearing zones
- FIG. 3 shows a flow chart of one embodiment of a method according to the present disclosure
- FIG. 4 shows a flow chart of another embodiment of a method according to the present disclosure
- FIG. 5 shows a simplified flow chart of a method for a clean formation according to one embodiment of the present disclosure.
- FIG. 6 shows a simplified flow chart of a method for using shear waves according to one embodiment of the present disclosure.
- FIG. 1 depicts a borehole 10 drilled in a typical fashion into a subsurface geological formation 12 to be investigated for potential hydrocarbon producing reservoirs.
- An NMR logging tool 14 has been lowered into the borehole 10 using a cable 16 and appropriate surface equipment (represented diagrammatically by a reel 18 ) and is being raised through the formation 12 comprising a plurality of layers 12 a through 12 g of differing composition, to log one or more of the formation's characteristics.
- the NMR logging tool may be provided with bowsprings 22 to maintain the tool in an eccentric position within the borehole with one side of the tool in proximity to the borehole wall.
- the permanent magnets 23 provide the static magnetic field.
- Signals generated by the tool 14 are passed to the surface through the cable 16 and from the cable 16 through another line 19 to appropriate surface equipment 20 for processing, recording, display and/or for transmission to another site for processing, recording and/or display.
- the processor may be located at a suitable position (not shown) downhole, e.g., in the logging tool 14 . It should be noted that the use of a wireline-conveyed NMR tool is for illustrative purposes only and the method of the present disclosure can be implemented using a logging tool conveyed on a bottomhole assembly by a drilling tubular.
- two models are used.
- One is a model relating acoustic measurements to formation porosity and the other is a model relating NMR measurements to an estimated formation porosity.
- the NMR model is discussed first.
- NMR ⁇ ⁇ ⁇ S w ⁇ I Hw ( 1 - e t w T 1 ⁇ ⁇ w ) + ⁇ ⁇ ( 1 - S w ) ⁇ I Hg ( 1 - e t w T 1 ⁇ ⁇ g ) , ( 1 )
- ⁇ is the formation porosity
- S w is the water saturation
- I Hw and I Hg are the hydrogen indices of water and gas respectively
- T lw and T lg are the longitudinal relaxation times of water and gas respectively
- t w is the wait time of the NMR pulsing.
- the NMR measurement made in a gas-free formation may be referred to as a “first measurement” made in a first interval.
- the present disclosure is illustrated using the Raymer-Hunt-Gardner (RHG) time transform, which is primarily developed for clean formations.
- the RHG transform for compressional wave can be written as:
- ⁇ acoustic ⁇ ⁇ ⁇ t p - ⁇ ⁇ ⁇ t p , ma ⁇ ⁇ ⁇ t p ⁇ C , ( 2 )
- ⁇ t p is the measured compressional wave slowness
- ⁇ t p,ma is the compressional wave slowness of the dry matrix
- C is a fitting parameter.
- the formation includes a first component (the matrix) that may be made of quartz, calcium carbonate or magnesium/calcium carbonate.
- ⁇ t ma can vary with the shale type, distribution, and percentage. This makes ⁇ t ma highly unpredictable for complex-lithology reservoirs.
- a basic assumption that is made is that within a certain depth interval, there is a good consistency of ⁇ t ma on the shale type and distribution. ⁇ t ma then only varies with fractional shale percentage and the fitting parameter C in the RHG transform is considered to be constant.
- NMR logs are used for calibration in the liquid-bearing zones to serve two main purposes.
- the Fractional Shale Volume can be estimated by one or more of the downhole measurement techniques, e.g., a Gamma Ray (GR) log, a spectral GR log, a Potassium-Thorium (KTh) log, a clay bound water (CBW) log, or an acoustic log that measures compressional wave velocity (V p ) and shear wave velocity (V s ), or a ratio between these velocities (V p /V s ).
- the CBW log is obtained using an NMR tool in the shaly interval.
- the Natural GR log which is mainly responsive to potassium, uranium, and thorium, has been widely used as shale indicator.
- the potassium spectrum log of the GR response is indicative of clay minerals.
- the uranium may exist in the hydrocarbon or biomass rather than in shale matrix.
- spectral GR logs which separately determine K, Th, and U, may be used as shale indicators and for quantifying shale volume.
- V shale GR - GR min GR max - GR min , ( 7 )
- GR is the Gamma Ray reading at each depth
- GR min is the minimal GR reading in the interval, often corresponding to the clay-free sand (i.e., clean sand)
- GR max is the GR reading from shale.
- the total GR in eqn. (7) can be the total GR, or one or more of the spectral GR components.
- CBW Volume of clay bound water (CBW) represents the porosity in clay or shale content in a formation rock. From NMR logs, both the fractional porosity from CBW ( ⁇ CBW ) and the total porosity ( ⁇ T,NMR ) may be obtained.
- NMR may be used to identify the fraction of shale content in a rock formation. If there is no shale content, then
- ⁇ CBW is usually determined by integration of the NMR signal corresponding to the relaxation time smaller than or equal to a pre-determined clay-bound water cutoff value: T 2 ⁇ T 2 cutoff (CBW) .
- T 2 ⁇ T 2 cutoff CBW
- the use of such criterion in carbonate formation should be with great caution, as the microporosity has the similar NMR relaxation time signature as that of clay bound water.
- V p /V s ratio varies with lithology of the formation and has been used as indicator of lithology based on “Pickett's crossplot”. Based on the current literature, V p /V s ratio of 1.9 is often used for limestones, 1.8 for dolostones, and in the range of 1.6 to 1.8 for clean sandstones. The shale content is also known to increase the V p /V s ratio compared to the value in the clean formation. Based on the Biot-Gassmann theory, the V p /V s ratio can be affected by porosity, fluid typing, lithology, etc.
- V p /V s can be considered as a good shale content indicator when the porosity is below 25 p ⁇ . It can be used in both sandstones and carbonates. More details on the related acoustic theory are attached in Appendix A.
- the primary acoustic porosity model used in this method is the RHG transform; the current disclosure comprises procedures using P-wave data and S-wave data.
- P-wave interpretation is the primary approach (compared to S-wave approach) and may be used for the formation with porosity less than 25 p ⁇ . It contains a method and procedure for determining the constant fitting parameter C and the matrix slowness. The matrix slowness varies with the shale content associated with any particular earth depth. The procedure can be summarized in the following three steps:
- a clean (i.e., shale-free) liquid-bearing sands logging interval is used in this step.
- the term “clean liquid bearing interval” refers to a liquid bearing zone with little shale content.
- the clean liquid bearing interval comprises a matrix of quartz, calcium carbonate or magnesium/calcium carbonate.
- HI of some liquid phase fluids in the formation may be slightly smaller than 1. Correction of HI for those fluids is generally known to be trivial and not expected to introduce significant error even if the fluid saturation is not highly accurate.
- C in the RHG are constant values, which are obtained simultaneously by fitting the RHG transform eqn. (2).
- the fitting parameter C is assigned to be the same for clean and shaly sands, base on the assumption that clay content does not drastically change the grain structure.
- Clean sands comprise primarily quartz.
- the assumption of a grain supported structure is valid if the clay is authigenic clay, which is only located in the pores or on the surface of grains. Such authigenic clay has little impact on the acoustic property in the grain supported structure.
- Authigenic clay is usually restricted to less than 40% of total volume. The clay forms the second component of the formation.
- the second step is to calculate ⁇ t p,ma for each depth in the zone of interest (gas bearing zone) by extracting the correlation between ⁇ t p,ma and the shale fraction.
- the estimation of FSV may be done using GR, CBW, or V p /V s ratio, or any combination of these, depending on the particular formation lithology, general porosity range, and data quality.
- the criteria for choosing the right candidate is described in the previous section: “The Fractional Shale Volume”.
- the values of the selected candidate as “x”. For instance, if we choose CBW, then “x” is
- x may be estimated from eqn. (7) or from a K log. If V p /V s is used, then “x” is the V p /V s ratio.
- ⁇ t p,ma In order to calibrate ⁇ t p,ma for a shaly sand formation, liquid-bearing zones with some shale contents are required. This can be either a shaly interval (V shale ⁇ 1) or full-shale interval (V shale ⁇ 1). There are two alternative approaches to calibrate ⁇ t p,ma depending on whether V shale ⁇ 1 or V shale ⁇ 1 is used for calibration.
- the correlation between ⁇ t p,ma and “x” in the clean and shaly zone is mapped.
- the matrix slowness in these zones can be back-calculated from Raymer-Hunt-Gardner by using C calibrated from the clean liquid-bearing zone:
- Polynomial functions can be used to provide a good fitting to the data trend, which may sometimes be a simple first order linear function.
- ⁇ t p,ma in the gas zone can be calculated by applying “x” at each depth into the fitting function. It should be noted that the notation herein makes a distinction between ⁇ t p,ma,clean for a clean dry matrix and ⁇ t p,ma,shale for a shale formation.
- FIG. 2 shows the plot of ⁇ t ma vs. GR in the water bearing zones, where ⁇ t ma is calculated using the fitting parameter C pre-calibrated in clean water-bearing zone in the first step of the calibration.
- ⁇ t ma a ⁇ GR+b (9).
- a formation-specific correlation can be used if sufficient historical log or core data in the substantial similar earth formation exist.
- ⁇ t ma and GR has the same correlation as shown in eqn. (9)
- ⁇ t ma in the gas-bearing zone can then calculated for each depth. An example is illustrated in FIG. 2 .
- the slowness of the rock matrix is a weighted average between the slowness of the clean matrix and the slowness of the shale, as shown in eqn.
- V shale is the FSV, which can be calculated from “x” corresponding the depth of the gas-bearing zone.
- V shale is the FSV, which can be calculated from “x” corresponding the depth of the gas-bearing zone.
- a linear correlation between V shale and “x” is used in the current method, although other correlation can be used as well. For instance, if GR is used for “x”, eqn. (7) is used to calculate V shale .
- parameters C and ⁇ t p,ma in the gas-bearing zone are known. Applying them into the RHG transform, eqn. (2), the porosity in the gas-bearing zone can be determined.
- This approach may be used for formation with porosity higher than 25 pu or when P-wave interpretation is not available.
- the S-wave-based interpretation also requires a calculation of the dry matrix slowness curve in the gas-bearing interval and further calculation of the porosity.
- the RHG equation for S-wave contains only one parameter ⁇ t s,ma , the first step in the P-wave interpretation for calibrating C is skipped.
- the S-wave interpretation procedure is similar to the procedure in P-wave interpretation, which is outlined below.
- ⁇ t s,ma (1 ⁇ T,NMR ) 2 ⁇ t s , (12) where NMR total porosity is used as the reference porosity in the water-bearing interval.
- a correlation between ⁇ t s,ma and curve “x” can then be established and by applying the same correlation into the gas-bearing interval, ⁇ t s,ma in the gas-bearing interval can be calculated.
- Calibration intervals may be selected for S-wave interpretation without clean-sand intervals. Unlike in P-wave interpretation, the parameter C may not be performed in S-wave interpretation.
- the constant C and the slowness ⁇ t p,ma in the clean water zone are determined 301 .
- the ⁇ t p,ma in the shaly water zone may be determined 303 . In the embodiment of FIG. 3 , this is done by establishing the correlation between ⁇ t p,ma and “x” 305 using the FSV.
- the fitting function found in 305 may be used to calculate ⁇ t p,ma in the gas bearing zone 307 .
- the acoustic porosity may be calculated using the calibrated C and ⁇ t p,ma 309 .
- Step 401 may be the same as steps 301 .
- ⁇ t p,ma,shale is obtained from ⁇ t p,ma,shale and ⁇ t fl 403 .
- the FSV “x” may be calculated for the gas bearing zone 405 .
- ⁇ t p,ma may be calculated 407
- the acoustic porosity may be calculated 409 .
- step 403 is implemented using ⁇ t p,ma,shale from a nearby shale zone.
- the estimated FSV may be sensitive to the value of GR min and GR max in eqn. (7). Consequently, in one embodiment, the average value of GR min in a clean formation is used and the average value of GR max in a shale zone is used.
- FIG. 5 shows an embodiment of the disclosure for use with clean formations.
- Step 501 is the same as steps 301 and 401 while step 503 is the same as steps 309 and 409
- FIG. 6 shows a flowchart of an embodiment of the disclosure using shear velocity measurements.
- a shear velocity log is obtained 601 . This may be done using any of suitable prior art devices for the purpose, for example, the device disclosed in U.S. Pat. No. 4,606,014 to Winbow.
- the value of ⁇ t s,ma in the water interval is calculated 603 .
- a correlation is established between ⁇ t s,ma and the selected curve.
- the value of ⁇ t s,ma in the gas-bearing interval is estimated 607 using the established correlation from 605 .
- the estimated value of ⁇ t s,ma in the gas-bearing interval may be used to calculate the porosity ⁇ 609 .
- a measurement is made by an acoustic tool that is indicative of the porosity of the formation. This measurement is made in an interval that includes a first solid component and also contains a second solid component and/or a gas. The porosity is then estimated using the acoustic measurement, a fractional value of shale (the second solid component) and the results of calibration of a measurement made by the acoustic tool in another interval that does not include gas. Depending on whether the acoustic measurement is of a compressional wave or a shear wave, the calibration may be characterized by one or two parameters.
- the results of the calibration may be stored in a table and a table look-up may be used to estimate the formation porosity using the acoustic measurement and the fractional shale volume.
- the method of the present disclosure is described above with reference to a wireline-conveyed NMR logging tool.
- the method may also be used on logging tools conveyed on coiled tubing in near horizontal boreholes.
- the method may also be used on NMR sensors conveyed on a drilling tubular, such as a drillstring or coiled tubing for Measurement-While-Drilling (MWD) applications.
- MWD Measurement-While-Drilling
- Implicit in the processing of the data is the use of a computer program implemented on a suitable machine-readable medium that enables the processor to perform the control and processing.
- the machine-readable medium may include ROMs, EPROMs, EAROMs, Flash Memories and Optical disks. These are all examples of non-transitory computer-readable media.
- V p /V s When acoustic wave propagates through formation rocks, the wave velocity ratio V p /V s varies with lithology of the formation and has been used as indicator of lithology based on “Pickett's crossplot”. Based on the current literature, V p /V s ratio is 1.9 for carbonate, 1.8 for dolomite, and in the range of 1.6 to 1.8 for clean sandstones. Using the grain contact theory Murphy et al. proposed in 1982, the calculated V p /V s ratio is 1.5 for sandstone, which has also been supported by experimental data on sandstones of a wide range of porosities. Castagna et al and Han et al observed that the clay content decreases the velocities of the acoustic wave, and proposed linear empirical correlations between the wave velocity ratio and FSV.
- the acoustic wave velocity for an isotropic, non-porous media is related to the frame moduli for the formation.
- the velocity of the compressional wave in a porous media can be written as:
- ⁇ c ⁇ V p 2 K p + K b + 4 ⁇ ⁇ 3
- K p is defined as pore space modulus
- ⁇ is the frame shear modulus
- K b is the frame bulk modulus
- K p ⁇ 2 ⁇ - ⁇ K m + ⁇ K f is the pore space modulus, where K m and K f are bulk moduli for matrix materials and fluid, respectively, ⁇ is porosity, and ⁇ is the Biot coefficient. At low porosities, or in dry sand,
- K b ⁇ 5 ⁇ ⁇ k n 3 ⁇ [ k n + 3 ⁇ ⁇ k t / 2 ] , where k n , k t are the normal and tangential stiffness of the grain contact. Murphy et al reported laboratory results that the
- K b ⁇ increases non-linearly with clay content, and approaching 2.0 in shale.
Abstract
Description
where φ is the formation porosity, Sw is the water saturation, IHw and IHg are the hydrogen indices of water and gas respectively, Tlw and Tlg are the longitudinal relaxation times of water and gas respectively, and tw is the wait time of the NMR pulsing. In gas-bearing formations logged with insufficient wait time, the low HI of the gas cause φt,NMR to be less than the true total porosity of the formation. The NMR measurement made in a gas-free formation may be referred to as a “first measurement” made in a first interval.
where Δtp is the measured compressional wave slowness, Δtp,ma is the compressional wave slowness of the dry matrix, and C is a fitting parameter. We note that C has low sensitivity to fluid typing, and is fairly stable and often can be treated as a constant. However, as the porosity increases, eqn. (2) becomes more sensitive to fluid typing.
where φ is the total porosity of the formation, Δts is the measured S-wave slowness in the formation, and Δts,ma is the S-wave slowness of the dry matrix. This equation assumes the S-wave modulus does not depend on the pore fluid.
where GR is the Gamma Ray reading at each depth, GRmin is the minimal GR reading in the interval, often corresponding to the clay-free sand (i.e., clean sand) and GRmax is the GR reading from shale. Note, the total GR in eqn. (7) can be the total GR, or one or more of the spectral GR components.
may be used to identify the fraction of shale content in a rock formation. If there is no shale content, then
and, if it is in a pure shale zone, then
φCBW is usually determined by integration of the NMR signal corresponding to the relaxation time smaller than or equal to a pre-determined clay-bound water cutoff value: T2≦T2 cutoff (CBW). However, the use of such criterion in carbonate formation should be with great caution, as the microporosity has the similar NMR relaxation time signature as that of clay bound water.
S liquid=1=>φacoustic=φT,NMR.
As noted above, the clean liquid bearing interval comprises a matrix of quartz, calcium carbonate or magnesium/calcium carbonate.
If GR is used, then “x” may be estimated from eqn. (7) or from a K log. If Vp/Vs is used, then “x” is the Vp/Vs ratio.
Polynomial functions can be used to provide a good fitting to the data trend, which may sometimes be a simple first order linear function. Finally Δtp,ma in the gas zone can be calculated by applying “x” at each depth into the fitting function. It should be noted that the notation herein makes a distinction between Δtp,ma,clean for a clean dry matrix and Δtp,ma,shale for a shale formation.
Δt ma =a·GR+b (9).
Δt p =Δt p,ma,shale(1−φT,NMR)+Δt flφT,NMR (10)
where Δtp,ma,shale and Δtfl are the shale and fluid slowness to calibrate the shale slowness Δtp,ma,shale The slowness of the rock matrix is a weighted average between the slowness of the clean matrix and the slowness of the shale, as shown in eqn. (11)
Δt p,ma =Δt p,ma,clean(1−V shale)+Δt p,ma,shale V shale, (11)
where Vshale is the FSV, which can be calculated from “x” corresponding the depth of the gas-bearing zone. A linear correlation between Vshale and “x” is used in the current method, although other correlation can be used as well. For instance, if GR is used for “x”, eqn. (7) is used to calculate Vshale.
Δt s,ma=(1−φT,NMR)2 ·Δt s, (12)
where NMR total porosity is used as the reference porosity in the water-bearing interval. A correlation between Δts,ma and curve “x” can then be established and by applying the same correlation into the gas-bearing interval, Δts,ma in the gas-bearing interval can be calculated. Calibration intervals may be selected for S-wave interpretation without clean-sand intervals. Unlike in P-wave interpretation, the parameter C may not be performed in S-wave interpretation.
and the velocity of the shear wave in a porous media is
ρcVs 2=μ
where Kp is defined as pore space modulus, μ is the frame shear modulus, and Kb is the frame bulk modulus.
where
is the pore space modulus, where Km and Kf are bulk moduli for matrix materials and fluid, respectively, φ is porosity, and α is the Biot coefficient.
At low porosities, or in dry sand,
and Kp→0. Thus
where kn, kt are the normal and tangential stiffness of the grain contact. Murphy et al reported laboratory results that the
ratio for clean sandstone (overgrowth dominated) is a constant value 0.9 independent from porosity, which form a lower bound for the ratio Vp/Vs=√{square root over (0.9+4/3)}=1.5, and stated the frame moduli
increases non-linearly with clay content, and approaching 2.0 in shale. However, there is no literature proposed any correlation between clay content and frame moduli ratio to further link to velocity ratio. Only empirical models have been reported such as the Castagna and Han's linear correlations between Vp/Vs ratio and FSV.
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PCT/US2011/055362 WO2012060974A2 (en) | 2010-10-25 | 2011-10-07 | An intergrated source-free method and apparatus for porosity determination: nmr calibrated acoustic porosity |
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US10267946B2 (en) | 2016-06-01 | 2019-04-23 | Baker Hughes, A Ge Company, Llc | Magnetic resonance pulse sequences having wait times based on carrier speed |
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Also Published As
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US20120101732A1 (en) | 2012-04-26 |
WO2012060974A2 (en) | 2012-05-10 |
NO20130048A1 (en) | 2013-01-22 |
GB2498104A (en) | 2013-07-03 |
GB201300790D0 (en) | 2013-02-27 |
BR112013010161A2 (en) | 2016-09-13 |
WO2012060974A3 (en) | 2012-08-02 |
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